Changing the scope of an IT migration from just BA to all of IAG makes the task significantly harder, but in the long term is the right thing to do - the CEO will likely salivate over all the potential long term "synergies" that can be achieved (job cuts to you and me)
That said, France and Germany are raising the question with the EU about BA being a non-EU carrier and what IAG should do about it - this is a strategic question of much greater urgency to a CEO than IT system re-engineering